The klezmer bandleader Eve Sicular is hardly a fan of J. Edgar Hoover, the F.B.I.’s first director, whose Cold War hunt for Communists put her grandmother in his sights. But he did keep meticulous records, and she can’t help being grateful for that.

“In a twisted archival way, Hoover did me a favor, making a scrapbook about Grandma,” Ms. Sicular says in her clever show “J. Edgar Klezmer: Songs From My Grandmother’s F.B.I. Files” — and could we pause for a moment, please, to savor that stellar title?

Featuring musicians from Ms. Sicular’s band, Isle of Klezbos, “J. Edgar Klezmer” is a kind of scrapbook, too. By turns playful and serious, it’s a musical piece of documentary theater assembled from old newspaper clippings, family photos, government documents and scavenged recollections about Adele Sicular, a New York physician who died in 1976, when her granddaughter was 14.

To the midcentury F.B.I., there was a whiff of subversion to this Russian-born Jewish doctor’s involvement with the Citizens Committee of the Upper West Side, a group whose name reliably cracked up the audience at Thursday night’s performance at Here Arts Center. Investigators interviewed neighbors and colleagues about Dr. Sicular’s loyalty to the United States.

A lively score — klezmer, jazz, boogie-woogie — is woven through the 60-minute show’s text, and when redacted documents are read aloud, blasts of musical notes replace the missing names. Smartly written and well structured, “J. Edgar Klezmer” draws clear parallels between the surveillance of Hoover’s America and our own, and it neatly avoids hagiography, thanks to a startling revelation by Ms. Sicular’s father, a character briefly in the show, that helps broaden the scope.

But the production, directed by Gwenyth Reitz, flattens the script. When Ms. Sicular is at her drum kit, playing with Shoko Nagai (piano) and Debra Kreisberg (clarinet and saxophone), she is in her element. But she is not an actor, and her discomfort at speaking her many lines is evident. The same is true of Melissa Fogarty, a lovely vocalist who is called on to act in multiple parts as well as to sing.

Yelena Shmulenson is the one actor in the cast, and she’s terrific. Her supple performance in a variety of roles suggests what this show could be, if actors were doing all the acting.